# Properties

 Label 16.6.a Level $16$ Weight $6$ Character orbit 16.a Rep. character $\chi_{16}(1,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $2$ Sturm bound $12$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$16 = 2^{4}$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 16.a (trivial) Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$12$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(\Gamma_0(16))$$.

Total New Old
Modular forms 13 3 10
Cusp forms 7 2 5
Eisenstein series 6 1 5

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$$2$$Dim.
$$+$$$$1$$
$$-$$$$1$$

## Trace form

 $$2q - 8q^{3} - 20q^{5} + 112q^{7} + 58q^{9} + O(q^{10})$$ $$2q - 8q^{3} - 20q^{5} + 112q^{7} + 58q^{9} - 664q^{11} + 60q^{13} + 2128q^{15} - 604q^{17} - 3880q^{19} + 576q^{21} + 3920q^{23} + 2142q^{25} - 2384q^{27} - 3876q^{29} + 1472q^{31} - 4000q^{33} + 2976q^{35} + 10028q^{37} - 14576q^{39} + 8340q^{41} + 21288q^{43} - 16964q^{45} - 22368q^{47} - 25294q^{49} + 31088q^{51} + 31180q^{53} - 19984q^{55} + 50848q^{57} - 9208q^{59} - 53220q^{61} - 4944q^{63} - 57944q^{65} - 6280q^{67} + 52928q^{69} + 78832q^{71} + 62676q^{73} - 49528q^{75} - 50496q^{77} + 32352q^{79} - 97742q^{81} - 135080q^{83} + 120728q^{85} + 58512q^{87} + 101748q^{89} - 25312q^{91} - 165632q^{93} + 180112q^{95} - 73532q^{97} + 33992q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(\Gamma_0(16))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 2
16.6.a.a $$1$$ $$2.566$$ $$\Q$$ None $$0$$ $$-20$$ $$-74$$ $$24$$ $$+$$ $$q-20q^{3}-74q^{5}+24q^{7}+157q^{9}+\cdots$$
16.6.a.b $$1$$ $$2.566$$ $$\Q$$ None $$0$$ $$12$$ $$54$$ $$88$$ $$-$$ $$q+12q^{3}+54q^{5}+88q^{7}-99q^{9}+\cdots$$

## Decomposition of $$S_{6}^{\mathrm{old}}(\Gamma_0(16))$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(\Gamma_0(16)) \cong$$ $$S_{6}^{\mathrm{new}}(\Gamma_0(4))$$$$^{\oplus 3}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_0(8))$$$$^{\oplus 2}$$